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Symmetry
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Mathematical Crystallography 2021
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Mathematical Crystallography 2021

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Chemistry: Symmetry/Asymmetry".

Deadline for manuscript submissions: closed (28 February 2023) | Viewed by 2454

Special Issue Editor

Prof. Dr. Sergey V. Krivovichev

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Guest Editor
1. Kola Science Center, Russian Academy of Sciences, Fersmana str. 14, 184209 Apatity, Russia
2. Department of Crystallography, Institute of Earth Sciences, St. Petersburg State University, University Emb. 7/9, 199034 St. Petersburg, Russia
Interests: mineralogy; crystallography; structural complexity; uranium
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Special Issue Information

Dear Colleagues,

Despite the enormous success of experimental crystallography achieved in the 20th century, the very problem of the emergence of order and symmetry in discrete structures is far from being completely understood. This Special Issue invites contributions on various mathematical aspects of modern crystallography, starting from diffraction theory and disorder and ending at deeply mathematical problems of symmetry, sphere packings, polyhedral, and discrete point sets.

Prof. Dr. Sergey V. Krivovichev
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • crystals
  • crystal structure
  • symmetry
  • long-range order
  • sphere packings
  • discrete point systems
  • polyhedral arrangements
  • lattices
  • space groups
  • quasicrystals

Published Papers (1 paper)

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Research

16 pages, 4427 KiB  
Article
Complexity of Molecular Nets: Topological Approach and Descriptive Statistics
by Alexander M. Banaru and Sergey M. Aksenov
Symmetry 2022, 14(2), 220; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14020220 - 24 Jan 2022
Cited by 10 | Viewed by 2136
Abstract
The molecular net complexity (HmolNet) is an extension of the combinatorial complexity (Hmol) of a crystal structure introduced by Krivovichev. It was calculated for a set of 4152 molecular crystal structures with the composition of Cx [...] Read more.
The molecular net complexity (HmolNet) is an extension of the combinatorial complexity (Hmol) of a crystal structure introduced by Krivovichev. It was calculated for a set of 4152 molecular crystal structures with the composition of CxHyOz characterized by the structural class P21/c, Z = 4 (1). The molecular nets were derived from the molecular Voronoi–Dirichlet Polyhedra (VDPmol). The values of the molecular coordination number (CNmol) and critical coordination number (CNcrit) are discussed in relation with the complexity of the crystal structures. A statistical distribution of the set of molecular crystals based on the values of CNmol, CNcrit, and the complexity parameters is obtained. More than a half of the considered structures has CNmol = 14 and CNmol′ = 9 with the Wyckoff set of edges e5dcba. The average multiplicity of intermolecular contacts statistically significantly decreases from 1.58 to 1.51 upon excluding all contacts except those bearing the molecular net. The normalized value of HmolNet is of the logistic distribution type and is distributed near 0.85HmolNet with a small standard deviation. The contribution of Hmol into HmolNet ranges from 35 to 95% (mean 79%, SD 6%), and the subset of bearing intermolecular contacts accounts for 41 to 100% (mean 62%, SD 11%) of the complexity of the full set of intermolecular contacts. Full article
(This article belongs to the Special Issue Mathematical Crystallography 2021)
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